Area of Shapes in the Plane
Primary 4 · Mathematics
Area of Shapes in the Plane
Lesson 3 of 5
30 min
Let's begin
Keza cuts a rectangular piece of cloth from corner to corner to make two triangular flags for the school sports day. "The two flags are exactly the same," she says. "So each flag is half of the cloth!"
Keza has found the secret of the area of a triangle. Let's see why it always works.
Cut a rectangle along its diagonal and you get two equal right-angled triangles. So each triangle has half the area of the rectangle.
This works for any triangle. Draw a rectangle around it with the same base and the same height. The triangle always fills exactly half of that rectangle.
Area of a triangle = base × height ÷ 2
Example: a flag has a base of 60 cm and a height of 40 cm. Area = 60 × 40 ÷ 2 = 2 400 ÷ 2 = 1 200 cm².
Example: a triangle has a base of 8 m and a height of 5 m. Area = 8 × 5 ÷ 2 = 40 ÷ 2 = 20 m².
Tip
Multiply, then halve. Base times height gives the rectangle; the triangle is half of it. Never forget the "÷ 2"!
Work each one in your exercise book first. Then tap Show answer to check.
A triangle has a base of 6 cm and a height of 4 cm. Find its area.
Answer: 12 cm², because 6 × 4 = 24 and 24 ÷ 2 = 12.
A right-angled triangle has the two short sides 10 m and 3 m, meeting at the right angle. Find its area.
Answer: 15 m², because 10 × 3 = 30 and 30 ÷ 2 = 15.
A rectangle is 12 cm by 5 cm. It is cut along a diagonal. What is the area of one triangle?
Answer: 30 cm², because 12 × 5 = 60 and 60 ÷ 2 = 30.
A triangle has a base of 9 cm and a height of 2 cm. Find its area.
Answer: 9 cm², because 9 × 2 = 18 and 18 ÷ 2 = 9.
Mugisha says a triangle with base 8 cm and height 4 cm has an area of 32 cm². What did he forget?
Answer: To divide by 2. The area is 16 cm².
What you learned today
Sources and credits
The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
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